Math Problem Statement

y=-3 x+y=9

Solution

To solve for xx in the system of equations:

  1. Substituting y=3y = -3 into the equation x+y=9x + y = 9:

x+(3)=9x + (-3) = 9

  1. Simplify:

x3=9x - 3 = 9

  1. Add 3 to both sides:

x=12x = 12

Solution:

x=12,y=3x = 12, \, y = -3

Do you have any questions, or would you like further details?

Here are 5 related questions to explore:

  1. How do you solve a system of linear equations with substitution?
  2. What are the graphical interpretations of these solutions?
  3. Can systems of equations have no solution or infinitely many solutions?
  4. What happens if you substitute yy with another value?
  5. How can we verify our solution?

Tip: Always check your solution by substituting the values back into the original equations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Substitution Method

Formulas

Substitution method: replacing a variable with its value in one equation to solve for the other variable

Theorems

Basic principle of equality and solving linear systems

Suitable Grade Level

Grades 6-8